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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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Journal ArticleDOI
TL;DR: In this article, the authors generalize the results of Drozdowicz, Popenda, and Migda and show that for every c G R there exists a solution of (Ε) convergent to c. The asymptotic behavior of solutions is investigated.
Abstract: (-E) Δχη = an q. We start our investigations with a useful lemma, given here without proof, which is elementary. LEMMA 1. Assume the series n l °n | is convergent and let rn = ί· Then the series n is absolutely convergent and ^Z^Li \" = η· THEOREM 1. Assume that the functions φ, ψ are continuous and the series Ση=ι n> Σ Γ = 1 are absolutely convergent. Then for every c G R there exists a solution of (Ε) convergent to c. P r o o f . Fix c e i ? . Choose a number a > 0. Let X = [c — a, c + a] χ [c — a, c + a].

9 citations

Proceedings ArticleDOI
23 May 1990
TL;DR: In this article, it was shown that the asymptotic inverse kinematic problem can be reduced to the problem of observing the state variables of a certain nonlinear dynamic system.
Abstract: It is shown that the asymptotic inverse kinematic problem can be reduced to the problem of observing the state variables of a certain nonlinear dynamic system. A simple asymptotic observer is used in the state estimation and the singular perturbation theory is used in the convergence proof of the algorithm. It is also shown that the classical methods of Newton and of the gradient can be obtained as particular asymptotic observers.

9 citations

Journal ArticleDOI
TL;DR: In this article, the asymptotic expansions of a wide class of Gaussian function space integrals are described and analyzed for both the nondegenerate case and the degenerate case.
Abstract: Function space integrals are useful in many areas of mathematics and physics. Physical problems often give rise to function space integrals depending on a parameter and the asymptotics with respect to the parameter yield important information about the original problem. The purpose of this note is to describe the asymptotic expansions of a wide class of Gaussian function space integrals. Related work has been done by [Varadhan], [Schilder], [Pincus], [Donsker-Varadhan], and [Castro]. All asymptotic expansions previously obtained assume a nondegeneracy condition which assures that one never strays too far from the realm of Gaussian processes. Our results cover both the nondegenerate case and the degenerate case, the analysis of the latter being much more subtle. In the degenerate case, the leading asymptotic behavior is non-Gaussian. Let PA be a mean zero Gaussian probability measure with covariance operator A on a separable Hubert space tf. Our methods can also handle certain Banach spaces, such as C[0, 1], which are important in applications. Let # and F be suitably bounded, real C°° functionals on H. We study the asymptotics of

9 citations

Book ChapterDOI
01 Jan 1979
TL;DR: In this article, the asymptotic behavior in K of the Kth order of the perturbative expansion has been investigated with remarkable success for both interacting bosons and fermions.
Abstract: During last year, the asymptotic behaviour in K of the Kth order of the perturbative expansion has been widely investigated with remarkable success1–3. If the interaction is superrenormalizable, the problem has been solved for both interacting bosons4, 5 and fermions6–8: of course technical details may change from theory to theory. When the interaction is renormalizable new difficulties arise9, 10; they are not completely understood at the present moment.

9 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526